The Chiral Case

Fig. 8. Diffraction space according to the "disordered stacking model" (a) achiral (zigzag) tube (b) chiral tube. The parallel circles represent the inner rims of diffuse coronae, generated by streaked reflexions. The oo.l nodes generate sharp circles. In (a) two symmetry related 10.0 type nodes generate one circle. In the chiral case (b) each node generates a separate corona [9].

The SmO and SmC phases have layered structures. In the SmC phase the molecular tilt in a layer is inclined at an angle to the layer normal and is the same in all layers. In SmO, the molecular tilt alternates in a herringbone pattern with equal and opposite tilts in neighboring layers. In the chiral case, the SmC and SmO phases have, in addition, a helix strueture, and so they are both helielectric, although SmO has a double-helix structure because of its herringbone structure. For a recent review of the SmO phase see A. Fukuda, Y. Takanishi, T. Isozaki, K. Ishi-kawa, H. Takezoe, J. Mater. Chem. 1994,4,997. 

As already pointed out, one condition for achieving the fast bistable switching and all the additional characteristic properties is to get rid of the antiferroelectric helix (to use the expression employed in the 1980 paper [93]). Therefore, achieving the same properties by adding appropriate chiral dopants to the smectic C could be imagined, in order to untwist the helical structure but, as the same time, keeping a residual polarization. This is illustrated by the structure to the left in Fig. 22. However, such a hypothetical bulk structure is not stable in the chiral case. It would transform to a twisted state where the twist does not take place from layer to layer, but in the layers, in order to cancel the macroscopic polarization. For this reason, surface-stabilization requires not only that dsample thickness is sufficiently small to prevent the ap-... 

The thermally excited cone motion, sometimes called the spin mode (this is very similar to the spin wave motion in ferromag-nets), or the Goldstone mode, is characteristic of the nonchiral SmC phase as well as the chiral SmC phase, but is of special interest in the latter because in the chiral case it couples to an external electric field and can therefore be excited in a controlled way. This Goldstone mode is of course the one that is used for the switching mechanism in surface-stabilized ferroelectric liquid crystal devices. The tilt mode, often, especially in the SmA phase, called the soft mode (although hard to excite in comparison with the cone mode, it may soften at a transition), is very different in character, and it is convenient to separate the two motions as essentially independent of each other. Again, this mode is present in the nonchiral SmA phase but cannot be detected there by dielectric methods, because a coupling to an electric field requires the phase to be chiral. In the SmA phase this mode appears as the electroclinic effect. 

Given the interest and importance of chiral molecules, there has been considerable activity in investigating die corresponding chiral surfaces [, and 70]. From the point of view of perfomiing surface and interface spectroscopy with nonlinear optics, we must first examhie the nonlinear response of tlie bulk liquid. Clearly, a chiral liquid lacks inversion synnnetry. As such, it may be expected to have a strong (dipole-allowed) second-order nonlinear response. This is indeed true in the general case of SFG [71]. For SHG, however, the pemiutation synnnetry for the last two indices of the nonlinear susceptibility tensor combined with the... 

Each act of proton abstraction from the a carbon converts a chiral molecule to an achi ral enol or enolate ion The sp hybridized carbon that is the chirality center m the start mg ketone becomes sp hybridized m the enol or enolate Careful kinetic studies have established that the rate of loss of optical activity of sec butyl phenyl ketone is equal to Its rate of hydrogen-deuterium exchange its rate of brommation and its rate of lodma tion In each case the rate determining step is conversion of the starting ketone to the enol or enolate anion... 

An alternative model has been proposed in which the chiral mobile-phase additive is thought to modify the conventional, achiral stationary phase in situ thus, dynamically generating a chiral stationary phase. In this case, the enantioseparation is governed by the differences in the association between the enantiomers and the chiral selector in the stationary phase. 

Although the chiral recognition mechanism of these cyclodexttin-based phases is not entirely understood, thermodynamic and column capacity studies indicate that the analytes may interact with the functionalized cyclodextrins by either associating with the outside or mouth of the cyclodextrin, or by forming a more traditional inclusion complex with the cyclodextrin (122). As in the case of the metal-complex chiral stationary phase, configuration assignment is generally not possible in the absence of pure chiral standards. 

A particular point of interest included in these hehcal complexes concerns the chirality. The heUcates obtained from the achiral strands are a racemic mixture of left- and right-handed double heUces (Fig. 34) (202). This special mode of recognition where homochiral supramolecular entities, as a consequence of homochiral self-recognition, result from racemic components is known as optical self-resolution (203). It appears in certain cases from racemic solutions or melts (spontaneous resolution) and is often quoted as one of the possible sources of optical resolution in the biological world. On the other hand, the more commonly found process of heterochiral self-recognition gives rise to a racemic supramolecular assembly of enantio pairs (204). 

Chiral nematic Hquid crystals are sometimes referred to as spontaneously twisted nematics, and hence a special case of the nematic phase. The essential requirement for the chiral nematic stmcture is a chiral center that acts to bias the director of the Hquid crystal with a spontaneous cumulative twist. An ordinary nematic Hquid crystal can be converted into a chiral nematic by adding an optically active compound (4). In many cases the inverse of the pitch is directiy proportional to the molar concentration of the optically active compound. Racemic mixtures (1 1 mixtures of both isomers) of optically active mesogens form nematic rather than chiral nematic phases. Because of their twist encumbrance, chiral nematic Hquid crystals generally are more viscous than nematics (6). 

Kinetic Resolutions. From a practical standpoint the principal difference between formation of a chiral molecule by kinetic resolution of a racemate and formation by asymmetric synthesis is that in the former case the maximum theoretical yield of the chiral product is 50% based on a racemic starting material. In the latter case a maximum yield of 100% is possible. If the reactivity of two enantiomers is substantially different the reaction virtually stops at 50% conversion, and enantiomericaHy pure substrate and product may be obtained ia close to 50% yield. Convenientiy, the enantiomeric purity of the substrate and the product depends strongly on the degree of conversion so that even ia those instances where reactivity of enantiomers is not substantially different, a high purity material may be obtained by sacrificing the overall yield. 

Unfortunately, assignment of molecules that are not closely related to the reference molecules becomes a subjective matter of assigning which substituents are similar. The application of the terminology to cases in which the chiral centers are not adjacent is also ambiguous. As a result, the threo-erythro terminology is not a general method of specifying stereochemical relationships. 

As seen in Table 2, many of the chiral tubules with d = 1 have large values for M for example, for the (6,5) tubule, M = 149, while for the (7,4) tubule, M = 17. Thus, many 2tt rotations around the tubule axis are needed in some cases to reach a lattice point of the ID lattice. A more detailed discussion of the symmetry properties of the non-symmorphic chiral groups is given elsewhere in this volume[8. ... 

An interesting feature of the synthesis is the use of allyl as a two-carbon extension unit. This has been used in the stereospecific synthesis of dicyclohexano-18-crown-6 (see Eq. 3.13) and by Cram for formation of an aldehyde unit (see Eq. 3.55). In the present case, mannitol bis-acetonide was converted into its allyl ether which was ozonized (reductive workup) to afford the bis-ethyleneoxy derivative. The latter two groups were tosylated and the derivative was allowed to react with its precursor to afford the chiral crown. The entire process is shown below in Eq. (3.59). 

NMR signals for difluoromethylene moieties range from -85 to -111 ppm (excluding difluorocyclopropyls), with viunal 7jjp values similar to the primary cases More compbcated sphttmg patterns arise from diastereotopic fluorines when a chiral center IS present in the gemmal difluonde Diastereotopic fluonnes may differ in chemical... 

The rhodium-catalyzed isomerization can also be carried out with the chiral catalyst, Ru2Cl4(diop)3 (H2, 20-80°, 1-6 h, 47-90% yield). In this case, optically enriched enol ethers are obtained. ... 

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